Issue 41

T. Vojtek et alii, Frattura ed Integrità Strutturale, 41 (2017) 245-251; DOI: 10.3221/IGF-ESIS.41.33 246 loading modes II and III by minimizing the extrinsic resistance by the preparation of fatigue precracks using cyclic compressive loading and subsequent annealing [10]. Such experiments revealed two basic types of closure-free propagation of mode II and mode III cracks in metallic materials [3]. First, the shear-mode propagation coplanar with precrack was observed for mode II loading in the case of bcc metals (e.g. ferritic steel or niobium) [11, 12]. In these materials, the dense set of slip planes in the bcc crystal lattice enabled creation and movement of dislocations in the slip planes lying sufficiently close to the plane of the maximum shear stress and thus possessing a high Schmid factor. The crack growth then proceeded along this plane in a nearly coplanar manner. The propagation of mode III cracks in the bcc metals was also found to be coplanar but the micromechanism revealed to be a spreading of in-plane tongues inclined by only very small angles to the macroscopic mode III crack front, thus driven by local mode II loading components [13]. These tongues mostly initiated on asperities (protrusions) of the microscopically tortuous crack fronts. The second (non- coplanar) type of crack growth was observed in materials with a low spatial density of slip systems (fcc) or with microstructural barriers for dislocation movement such as the pearlitic steel. In these materials, the fronts of the mode II cracks immediately deflected from the shear plane to experience a pure mode I loading whereas the mode III crack fronts locally twisted to create mode I segments which could lead to a formation of the factory-roof morphology. The growth mechanism in hcp materials represented a transition between the above mentioned two principal types [14, 15]. Thus, for the same specimen geometry and the same kind of shear-mode loading, different materials exhibit different crack paths. However, just a combination of local mode I and local mode II growth mechanisms is relevant for description of behaviour of most metallic materials [3, 12, 13] under all kinds of shear-modes (II, III and II+III). The classical criteria for mixed-mode crack propagation [16 – 18] do not take these differences into account and do not reflect the physical nature of the process. Such criteria cannot be reliably applied to mode II and mode III crack growth since there is no local mode III growth mechanism adequately efficient with respect to that of the mode II [19, 20]. The cracks grow under local mode I or II mechanisms instead [15, 21]. To apply the approach of local growth mechanism it is necessary to determine the local SIFs for the spatially oriented crack fronts. Such analysis was already done for remote mode II cracks [15]. The results led to a formulation of predictive relationship for the effective mode II threshold, which was verified by experimentally measured values. In the case of mode III cracks, however, the analysis is much more difficult due to the complicated mechanisms of local mode II crack advances or factory roof formation. Therefore, no quantitative expression for prediction of the effective mode III threshold was found hitherto. The present paper addresses the problem of the prediction of effective mode III threshold for the ARMCO iron as a case study of materials with coplanar shear-mode crack propagation. For such materials, the 2D (in-plane) modelling of the tortuous crack geometry is sufficiently relevant and, therefore, the finite element analysis of the local mode II component for a crack with serrated (zig-zag) front loaded in the remote mode III was performed. The results are useful for expression of the ratio k 2 / K III of local mode II SIF to the global mode III SIF for a straight crack front, which can be compared with the experimentally measured ratio of effective thresholds Δ K IIeff,th and Δ K IIIeff,th . M ATERIAL AND E XPERIMENTS xperimental data were evaluated for the ARMCO iron which is a nearly pure ferrite, as a representative of pure bcc metals. The mode III fatigue crack propagation experiment was performed using specimens cyclically loaded in torsion. The cylindrical specimens had a circumferential notch with the outer diameter D = 25 mm and the inner diameter d = 12 mm. A detailed description of the experimental arrangement can be found in [10]. The precracks were generated at the notch root by cyclic compressive loading [22 – 24] which resulted in an open precrack and avoided closure effects such as friction and contact of the fracture surfaces. After precracking the specimens were annealed in vacuum in order to eliminate the plastic zone in the vicinity of the crack tip and to avoid creation of an oxide layer. In this way, the effective (closure-free) mode III crack propagation threshold was measured. After applying N = 10 5 loading cycles with the cyclic stress ratio R = 0.1 at room temperature the experiments were stopped and the specimens were fractured by cyclic push-pull loading in mode I. The fracture surfaces were observed in the scanning electron microscope (SEM), where the crack length was measured. N UMERICAL MODEL o evaluate local stress intensity factors along the tortuous precrack front a finite element model [25] created with ANSYS finite element modeller was adapted. Because of the applied loading and the geometry of the specimen a full 3D model had to be used for the torsion specimen and one symmetry plane was used for the shear specimen. E T